Agricultural Drought Indices - US Department of Agriculture

The purpose of the climatic characteristic, K, is to adjust the value of d according to the
characteristics of the climate in such a way as to allow for accurate comparisons of PDSI values
over time and space. The result of multiplying the moisture departure, d, by K is called the
moisture anomaly index, or the Z Index. The Z index can be used to show how wet or dry it was
during a single month without regard to recent precipitation trends. The Z index is used to
calculate the PDSI value for a given month using the general formula:
X i = 0.897 X i-1 + 1/3 Z i
Palmer called the values 0.897 and 1/3 the duration factors. They were empirically derived by
Palmer from two locations (western Kansas and central Iowa) and affect the sensitivity of the index
to precipitation events. Three PDSI values are actually computed each month: X 1 , X 2 , and X 3 . The
values of X 1 and X 2 are the severity of a wet or dry spell, respectively, that might become
established. A spell becomes established when it reaches the threshold of ±0.5. This threshold
follows from the fact that index values between -0.5 and 0.5 are regarded as ‘‘normal’’ values; X 3 is
the severity of a wet or dry spell that is currently established. If no spell is established, the PDSI
value is set to either X 1 or X 2 , according to which spell is most likely to become established. This
is determined by which index is closer to the threshold of an established spell, which is simply the
index with a larger absolute value. If a current spell is established (i.e., when X 3 is not zero), the
PDSI value for that month is X 3 . However, when the index is calculated at a later date, it may be
discovered that the current spell actually ended earlier. In this case, the PDSI values will be
replaced by values of either X 1 or X 2 . This replacement of previously calculated PDSI values will
be referred to as backtracking. The existence of backtracking means that a small change in how
the indices are computed may cause backtracking, which has a substantial effect on the final
values of the index.
Self-Calibrated Palmer Drought Severity Index (sc-PDSI)
The scPDSI is a variant of the original PDSI of Palmer (1965), with the aim of making results from
different climate regimes more comparable (Wells et al. 2004). As described by Wells et al., the
scPDSI is calculated from a time series of precipitation and temperature, together with a set of
calibrated empirical constants. The process of replacing all empirical constants in Palmer’s
procedure for calculating the sc-PDSI results in a process that is slightly more complicated than
before. The steps required to calculate scPDSI include the following:
1) Calculate all moisture departures.
2) Calculate all moisture anomalies.
3) Calculate the duration factors, using the moisture anomalies computed in step 2.
4) Calculate the PDSI using the moisture anomalies and duration factors computed in steps 2 and
3, respectively.
5) Find the 98 th and 2 d percentile values of the PDSI.
6) Compute the new moisture anomalies.
7) Calculate the SC-PDSI.
This is a more computationally intensive process than Palmer’s original procedure. However, the
power of the current generation of computers means that the PDSI can be calculated in a matter of
seconds, even for stations with more than a hundred years of data.
Using the redefined climatic characteristics and a set of duration factors derived in the described
manner to calculate the PDSI has several positive consequences:
• The range of the PDSI values is close to an expected range of 25.0 to 5.0, where values
below 24 and above 4 represent extreme conditions.
• The sensitivity of the index is based upon the local climate.
• Different sensitivity to moisture and lack of moisture.
• The PDSI can be updated at different time intervals (e.g., weekly, biweekly, monthly).
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